Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 5
Level $[5, 5, w + 2]$
Label 2.2.85.1-5.1-a
Dimension 6
CM no
Base change yes

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Base field \(\Q(\sqrt{85}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).

Form

Weight [2, 2]
Level $[5, 5, w + 2]$
Label 2.2.85.1-5.1-a
Dimension 6
Is CM no
Is base change yes
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut 8x^{4} \) \(\mathstrut +\mathstrut 16x^{2} \) \(\mathstrut +\mathstrut 4\)

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Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $\phantom{-}e^{2} + 1$
5 $[5, 5, w + 2]$ $-\frac{1}{2}e^{3} - 2e$
7 $[7, 7, w]$ $\phantom{-}e^{5} + 7e^{3} + 11e$
7 $[7, 7, w + 6]$ $\phantom{-}e^{5} + 7e^{3} + 11e$
17 $[17, 17, w + 8]$ $-2e^{3} - 10e$
19 $[19, 19, w + 1]$ $-e^{4} - 4e^{2}$
19 $[19, 19, w - 2]$ $-e^{4} - 4e^{2}$
23 $[23, 23, w + 9]$ $-2e^{5} - 12e^{3} - 13e$
23 $[23, 23, w + 13]$ $-2e^{5} - 12e^{3} - 13e$
37 $[37, 37, w + 11]$ $-e^{5} - 8e^{3} - 12e$
37 $[37, 37, w + 25]$ $-e^{5} - 8e^{3} - 12e$
59 $[59, 59, 3w + 10]$ $-e^{4} - 6e^{2} - 4$
59 $[59, 59, 3w - 13]$ $-e^{4} - 6e^{2} - 4$
73 $[73, 73, w + 15]$ $-5e^{3} - 22e$
73 $[73, 73, w + 57]$ $-5e^{3} - 22e$
89 $[89, 89, -w - 10]$ $\phantom{-}5e^{4} + 25e^{2} + 14$
89 $[89, 89, w - 11]$ $\phantom{-}5e^{4} + 25e^{2} + 14$
97 $[97, 97, w + 22]$ $\phantom{-}e^{5} + 10e^{3} + 18e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w + 2]$ $\frac{1}{2}e^{3} + 2e$